A modeling method for a transient sensitization mathematical model of stainless steel

Abstract

The application relates to a modeling method for a transient sensitization mathematical model of stainless steel. The model obtained by the method can accurately evaluate the sensitization degree of a component during heat treatment, so that corresponding measures can be taken in time, and corrosion tendency is reduced. The technical scheme is as follows: a modeling method for a transient sensitization mathematical model of stainless steel, comprising the following steps: S1: dividing stainless steel samples into multiple groups, and setting different heat treatment parameters; S2: after surface treatment of the samples after heat treatment, correlating C content, Cr content, heating temperature and holding time to obtain data of the samples in each group; S3: establishing an expression of the transient sensitization model of the stainless steel; S4: fitting the data of the samples in each group obtained in step S2 with a function; obtaining a function under temperature T t ; by substituting and T t into the expression, a function under temperature T t can be obtained; S5: substituting the fitting function into the expression to obtain a final transient sensitization mathematical model.

Description

Technical Field

[0001] The invention relates to a stainless steel heat treatment method, in particular to a modeling method for a transient sensitization mathematical model of stainless steel. Background Art

[0002] TP347H stainless steel is an austenitic stainless steel containing stabilizing elements. It is widely used in nuclear power plants, chemical industry, oil and gas transportation and other fields due to its good high temperature oxidation resistance, wear resistance, corrosion resistance and thermal stability. When TP347H austenitic stainless steel is sensitized within the temperature range of 400-850℃, high chromium carbide Cr will be formed. 23 The precipitation of C6 at grain boundaries creates chromium-depleted regions between grains, which can easily lead to intergranular corrosion. This is the sensitization phenomenon in stainless steel. Because intergranular corrosion has no obvious characteristics and is difficult to detect, it can cause sudden damage to equipment and pose a significant risk. Therefore, a transient sensitization mathematical model for TP347H stainless steel was developed to evaluate its degree of sensitization. Summary of the Invention

[0003] The purpose of the present invention is to overcome the shortcomings of the above-mentioned background technology and provide a modeling method for the transient sensitization mathematical model of stainless steel. The model obtained by this method can accurately evaluate the sensitization degree of the component during heat treatment, so as to take timely countermeasures and reduce the corrosion tendency.

[0004] The technical solution adopted by the present invention is as follows: a modeling method for a transient sensitization mathematical model of stainless steel, comprising the following steps:

[0005] S1: Divide the stainless steel samples into multiple groups and set different heat treatment parameters. The samples in the same group are heated to the same temperature but have different holding times for aging treatment.

[0006] S2: After surface treatment of the heat-treated samples, the C and Cr contents at the grain boundaries were obtained using an energy spectrometer. The C content, Cr content, heating temperature, and holding time were correlated to obtain data for each group of samples.

[0007] S3: Establishing the expression of the transient sensitization model of stainless steel

[0008]

[0009] Where: x Cr Indicates Cr concentration; function is a point at a distance x from the grain boundary at temperature T t Cr content function at time t;

[0010] S4: Use the data and function of each group of samples obtained in step S2 Fitting; get temperature Tt The following function For:

[0011]

[0012] Will and T t Substitution The expression of the corresponding temperature T can be obtained t The following function

[0013] S5: Function Substitute the fitting expression into

[0014] The final transient sensitization mathematical model is obtained:

[0015]

[0016] x Cr is the actual Cr content at a point near the grain boundary; t is the growth time; T is the diffusion temperature;

[0017] is the initial Cr content of stainless steel; τ is the time required to achieve complete sensitization;

[0018] k is a preset constant parameter; represents the Cr content in the form of carbides;

[0019] L0 represents the width of the Cr concentration reduction area, which is a preset constant;

[0020] x is the distance between the actual test position of a certain point and the grain boundary;

[0021] D0 is the diffusion constant; Q is the diffusion activation energy of Cr, which is a constant; and R is the molar constant.

[0022] Preferably, 7 groups of samples are established, with the heating temperature ranging from 500°C to 800°C in steps of 50°C.

[0023] Preferably, the sample size is 10 mm×10 mm×5 mm.

[0024] Preferably, the holding time of aging treatment at 500°C is: 10h, 20h, 50h, 100h respectively;

[0025] The holding times for aging treatment at 550℃ are: 10h, 20h, 50h, 100h;

[0026] The holding time for aging treatment at 600℃ is: 1h, 2h, 4h, 10h, 20h, 40h, 70h, 100h; the holding time for aging treatment at 650℃ is: 1h, 2h, 4h, 10h, 20h, 40h, 70h, 100h; the holding time for aging treatment at 700℃ is: 1h, 2h, 4h, 10h, 20h, 40h, 70h, 100h; the holding time for aging treatment at 750℃ is: 1h, 2h, 4h, 10h, 20h, 40h, 70h, 100h; the holding time for aging treatment at 800℃ is: 10h, 20h, 50h, 100h.

[0027] The application method of the transient sensitization mathematical model is: substituting different heat treatment temperatures and durations into the transient sensitization model to obtain the Cr content near the grain boundary and determine whether the stainless steel is sensitized. If sensitization occurs, it indicates that the corrosion resistance is reduced; otherwise, it indicates that the corrosion resistance is qualified.

[0028] The beneficial effect of the present invention is that the provided method for constructing a transient sensitization mathematical model for stainless steel can not only obtain the temperature at any position of the stainless steel component, but also obtain the temperature field distribution at any position that changes with time. Therefore, it can be used simply and accurately to detect the sensitization phenomenon and the degree of sensitization generated by the stainless steel component after it has passed through the entire sensitization temperature range during the heat treatment process, and effectively prevent the harm caused by intergranular corrosion of the material. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a flow chart of a modeling method of a transient sensitization mathematical model of stainless steel according to an embodiment of the present invention.

[0030] Figure 2 This is a scanning electron microscope photograph of the grain boundary morphology of the sample after heat treatment in an embodiment of the present invention.

[0031] Figure 3 3 is a schematic diagram of an energy spectrometer line scan analysis along the normal direction of the grain boundary according to an embodiment of the present invention.

[0032] Figure 4 This is an embodiment of the present invention Figure 3 Element composition ratio diagram at the grain boundaries.

[0033] Figure 5 This is an embodiment of the present invention Figure 3 Cr concentration variation curve in the normal direction of the grain boundary.

[0034] Figure 6 This is an embodiment of the present invention Figure 3 C concentration variation curve in the normal direction of the grain boundary.

[0035] Figure 7This is a scanning electron microscope photograph of the grain boundary of a TP347H stainless steel sample of an embodiment of the present invention, which was operated for 2 years and 5 months at an operating temperature of 620°C.

[0036] Figure 8 In the embodiment of the present invention Figure 7 The energy spectrometer point scanning data results at the crystal and hole grain boundaries. DETAILED DESCRIPTION

[0037] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be further described in detail below with reference to the embodiments. However, it should be understood that these descriptions are only exemplary and are not intended to limit the scope of the present invention.

[0038] The present invention provides a modeling method for a transient sensitization mathematical model of stainless steel as follows:

[0039] Stainless steel samples were divided into multiple groups and different heat treatment parameters were set. The samples in the same group were heated at the same temperature but held for different times. After the heat-treated sample surfaces were ground and polished until no scratches were left, the C and Cr contents at the grain boundaries were obtained using an energy dispersive spectrometer in a scanning electron microscope system. The C content, Cr content, heating temperature, and holding time were correlated to form data for each group of samples. After the treated sample surfaces were ground and polished until no scratches were left, the chemical composition changes at the grain boundaries were analyzed using an energy dispersive spectrometer in a scanning electron microscope system. The expression for the transient sensitization model of stainless steel was established: where x Cr Represents Cr concentration, function is the position at the distance x from the grain boundary and the Cr content function at time t under temperature Tt; using the data of each group of samples and the function Fitting; fitting the function Substitute the fitting expression into The final transient sensitization mathematical model is obtained:

[0040]

[0041] x Cr is the actual Cr content at a certain point near the grain boundary; t is the growth time; T is the diffusion temperature;

[0042] is the initial Cr content of stainless steel; τ is the time required to achieve complete sensitization;

[0043] k is a preset constant parameter; represents the Cr content in the form of carbides;

[0044] L0 represents the width of the Cr concentration reduction area, which is a preset constant;

[0045] x is the distance between the actual test position and the grain boundary;

[0046] D0 is the diffusion constant; Q is the diffusion activation energy of Cr, which is a constant; and R is the molar constant.

[0047] The function is obtained by using each set of data The fitting method is as follows:

[0048] During the initial carbide precipitation stage, the chromium concentration distribution at the grain boundaries is expressed by the following equation:

[0049]

[0050] Where:

[0051] τ is the time required to achieve complete sensitization (when t≤70h, τ=70h; when t>70h, τ=t),

[0052] It can be regarded as the Cr content in non-compound form, k is a preset constant parameter, is the initial Cr content of stainless steel, according to Calculated The k value obtained by fitting;

[0053] The chromium concentration distribution at the grain boundary can be regarded as the conservation of mass flow through the interface, that is, the spontaneous exchange of chromium atoms at the interface between the grain and the carbide. The intermediate quantity S1 represents the concentration of Cr carbides precipitated near the grain boundary. The value of S1 is obtained by energy spectrometer detection. represents the Cr content in the form of carbides;

[0054] Since the growth of carbides is restricted by the diffusion of chromium atoms inside the grains, their size r can be expressed as: Where β is a preset constant and D is the diffusion coefficient of chromium, which can be calculated as follows:

[0055]

[0056] At time τ, the concentration of chromium atoms at the grain boundaries reaches its minimum value, and the precipitation of Cr carbides slows down and can be ignored. At this time, S1 can be expressed as: Fit the value of S1 to obtain the corresponding T t Next

[0057] The chromium concentration at the grain boundary at time τ can be considered to be linear; the intermediate value S2 of the Cr concentration distribution at this time is:

[0058] Where: erf() is the error function, which can be expressed as follows:

[0059] L0 is a preset constant, indicating the width of the Cr concentration reduction region; it is larger than or equal to the width of the chromium-depleted region, and is equivalent to half the grain size;

[0060] The finite difference method can be used to accurately calculate S2:

[0061] Where, the value of xj varies between 0 and L0:

[0062]

[0063]

[0064]

[0065] Get the function at temperature Tt For:

[0066] Will and Tt into The expression of can be used to obtain the function corresponding to the temperature Tt

[0067] The function Substitute the fitting expression into The following transient sensitization mathematical model is obtained:

[0068]

[0069] The method of using the present invention is to substitute different heat treatment temperatures and durations into the transient sensitization model to obtain the Cr content near the grain boundary and determine whether the stainless steel is sensitized. If sensitization occurs, it indicates that the corrosion resistance is reduced; otherwise, it indicates that the corrosion resistance is qualified.

[0070] Example 1

[0071] In this example, TP347H stainless steel was used as a sample and a transient sensitization mathematical model was established. Seven groups of samples were established, and the heating temperature ranged from 500° C. to 800° C. in steps of 50° C. The sample size was 10 mm × 10 mm × 5 mm.

[0072] Figure 2 This is a scanning electron microscope photo of the grain boundary morphology of the sample after heat treatment. Figure 2 On the grain boundary, the energy spectrometer line scan analysis is performed along the normal direction of the grain boundary, such as Figure 3 As shown by arrow 1 in the figure. The content of each element at the grain boundary position analyzed by energy spectrometer is as follows Figure 4 As shown; Specifically, based on the C content, it is inferred that high chromium carbide Cr23 The content of C6 can be used to calculate the concentration of Cr in the form of carbides. Figure 3 The results of the energy spectrum analysis along the normal direction of the grain boundary can also be used to obtain the changes in the Cr concentration and C concentration along the normal direction of the grain boundary (the direction of arrow 1 in the figure). The Cr concentration change curve along the normal direction of the grain boundary is shown in Figure 5 (The direction of the horizontal axis arrow in the figure is Figure 3 The direction of the arrow 1 in the figure is consistent), and the C concentration change curve along the normal direction of the grain boundary is shown in Figure 6 (The direction of the horizontal axis arrow in the figure is Figure 3 The direction of arrow 1 is the same as in the figure).

[0073] In this example, a TP347H stainless steel sample with an operating time of 2 years and 5 months and an operating temperature of 620°C was selected. The preset constant K = -3.84 was obtained by fitting the previous experimental data.

[0074] Other calculation constants in the formula are

[0075]

[0076] L0=5μm

[0077] X=2μm

[0078] D0=0.83

[0079] Q=244kJ / mol

[0080] R=8.314

[0081] Because t>70h, we take τ=20880h (2 years and 5 months);

[0082] Will k, L0, x, D0, Q, R, τ, as well as T = 620 ° C and t = 20880 h are substituted into the following transient sensitization mathematical model,

[0083]

[0084] You will get:

[0085] Through the transient sensitization mathematical model, it was calculated that the Cr element content near the grain boundary was only 12.86wt%, and the grain boundary showed obvious chromium depletion, indicating that sensitization phenomenon had already occurred near the grain boundary.

[0086] Figure 7 These are two scanning electron microscope photos of the sample, showing that large-scale dense holes appear at the grain boundaries. Figure 8 for Figure 7The energy spectrum detection data results of the grain boundary interior and grain boundary holes 1, 2, and 3 in the scanning electron microscope image; among them, Figure 7 Energy spectrum data from a central pore indicates a distinct Cr- and Ni-depleted region. The Cr and Ni contents in this region are only 13.74wt% and 2.22wt%, respectively, significantly lower than the 18.07wt% and 8.43wt% found within the normal austenite grains. This indicates that the sample has undergone severe sensitization. The data are generally consistent with the results calculated using the transient sensitization mathematical model, validating the accuracy of the model.

[0087] The present invention studies the sensitization characteristics at different temperatures and substitutes them into the temperature variable to establish a transient sensitization characteristic model. This model can be used to evaluate the sensitization degree of stainless steel during temperature changes and prevent engineering losses caused by intergranular corrosion.

[0088] The above shows and describes the basic method, main features and advantages of the present invention. Those skilled in the art should understand that the device of the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications are possible without departing from the spirit and scope of the present invention, and such changes and modifications fall within the scope of the invention as claimed.

Claims

1. A modeling method for a transient sensitization mathematical model of stainless steel, comprising the following steps: S1: Divide the stainless steel samples into multiple groups and set different heat treatment parameters. The samples in the same group have the same heating temperature but different aging treatment time and holding time. S2: After surface treatment of the heat-treated samples, the C and Cr contents at the grain boundaries were obtained using an energy spectrometer. The C content, Cr content, heating temperature, and holding time were correlated to obtain data for each group of samples. S3: Establishing the expression of the transient sensitization model of stainless steel in: Represents Cr concentration; function is a point at a distance x from the grain boundary at temperature T t Cr content function at time t; S4: Use the data and function of each group of samples obtained in step S2 Fitting to obtain temperature T t The following function For: ， Will and T t Substitution The expression of the corresponding temperature T can be obtained t The following function ; S5: Function Substitute the fitting expression into The final transient sensitization mathematical model is obtained: Where: is the actual Cr content at a certain point near the grain boundary; t is the growth time; T is the diffusion temperature; is the initial Cr content of stainless steel; τ is the time required to achieve complete sensitization; represents the Cr content in the form of carbides; k is a preset constant parameter; L0 represents the width of the Cr concentration reduction area, which is a preset constant; x is the distance between the actual test position of a certain point and the grain boundary; D0 is the diffusion constant; Q is the diffusion activation energy of Cr, which is a constant; R is the molar constant.

2. The modeling method for the transient sensitization mathematical model of stainless steel according to claim 1, characterized in that: There are 7 groups of samples, and the heating temperature ranges from 500°C to 800°C with a step of 50°C.

3. The modeling method for the transient sensitization mathematical model of stainless steel according to claim 2, characterized in that: The sample size is 10 mm×10 mm×5 mm.

4. The modeling method for the transient sensitization mathematical model of stainless steel according to claim 3, characterized in that: The temperature and holding time of the aging treatment are: The temperature and time of aging treatment at 500℃ are: 10h, 20h, 50h, 100h; The holding times for aging treatment at 550℃ are: 10h, 20h, 50h, 100h; The holding time for aging treatment at 600℃ is: 1h, 2h, 4h, 10h, 20h, 40h, 70h, 100h; the holding time for aging treatment at 650℃ is: 1h, 2h, 4h, 10h, 20h, 40h, 70h, 100h; the holding time for aging treatment at 700℃ is: 1h, 2h, 4h, 10h, 20h, 40h, 70h, 100h; the holding time for aging treatment at 750℃ is: 1h, 2h, 4h, 10h, 20h, 40h, 70h, 100h; the holding time for aging treatment at 800℃ is: 10h, 20h, 50h, 100h.

5. The modeling method for the transient sensitization mathematical model of stainless steel according to claim 4, characterized in that: The surface treatment is to grind and polish the surface of the sample until there is no scratch.

6. The modeling method for the transient sensitization mathematical model of stainless steel according to claim 5, wherein The characteristic is that the application method of the transient sensitization model is: different heat treatment temperatures and durations are substituted into the transient sensitization model to obtain the Cr content near the grain boundary and judge whether the stainless steel is sensitized. If so, Sensitization indicates that the corrosion resistance is reduced, otherwise it indicates that the corrosion resistance is qualified.

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